In few-cycle pulses, the exact value of the carrier-envelope phase difference (CEPD) has a pronounced influence on the ionization dynamics of atoms and molecules. We show that for atoms in circularly polarized light, a change in the CEPD is mapped uniquely to an overall rotation of the system, and results for arbitrary CEPD are obtained by rotation of the results from a single calculation with fixed CEPD. For molecules this is true only for linear molecules aligned parallel with the propagation direction of the field. The effects of CEPD are classified as geometric or non-geometric. The observations are exemplified by strong-field calculations on hydrogen.